**Iryna**
**YEHORCHENKO**

**Address:**

Institute
of Mathematics

National
Academy
of Sciences
of Ukraine

3
Tereshchenkivs'ka Street

01024
Kyiv

UKRAINE

**E-mail:**
iyegorch@imath.kiev.ua

**Academic
Background:** *Ph.D.
in Math.*:
1989, Institute of Mathematics, Kyiv (Supervisor Prof. W.I.
Fushchych) Symmetry
analysis of nonlinear equations for complex scalar and vector
fields*M.Sc.
in Math.*:
1984, Kyiv National
University

**Professional
Experience:** *1985-till
now*

Senior
Researcher
at the Department of
Applied Research of
the Institute of
Mathematics, National Academy of
Sciences, Kyiv

ORCID 0000-0001-6442-4812

**AREA** **OF
EXPERTISE:** mathematical
physics, symmetry analysis of PDE; Lie algebras and Lie groups;
symmetry, reduction and exact solutions of nonlinear PDE; nonlocal,
potential and nonclassical symmetries of PDE; point transformations
and equivalence problems in classes of PDE; theory of differential
invariants

**MOST
IMPORTANT RESEARCH RESULTS**:
classification of differential invariants of the Euclid, Poincare,
Lorentz, conformal, Galilei algebras for arbitrary dimensions and
arbitrary sets of scalar functions; definition and study of
conditional differential invariants; efficient procedure for
classification of relative differential invariants, concept of
extension for realizations of first-order differential operator
algebras; classification of invariant equations and analytical
solutions for equations of mathematical physics; necessary conditions
of compatibility of the d’Alembert and Hamilton equations for
arbitrary dimensions and one and two functions; general solution of
the system of coupled eikonal equations; differential invariants of
the nonlinear realisation of the Poincare algebra; efficient
procedure for classification of differential invariants of
infinite-dimensional algebras; general parametric solutions of many
nonlinear systems of PDE. Presented talks at over 50 international
conferences.

**Other
activities:**

Member of the Organising Committee of the conferences ``Symmetry in Nonlinear Mathematical Physics''

(Kyiv, Ukraine, 1995, 1997, 1999, 2001, 2003, 2005, 2007, 2009)

Associate Editor, SIGMA

Member of the Organising Committee of the Voronoi Conferences (Kyiv, Ukraine, 1993, 1998, 2003, 2008, 2013, 2018)

Reviewer, Mathematical Reviews

Presented talks at numerous international conferences on evaluation of research and research policies. Founder and member of two NGOs working in promoting of good practices in science and education, and improvement of policies in these fields; and in attraction of girls to STEM professional fields. Participated in numerous working groups at the NASU and Parliament of Ukraine on science and education policies. Taught at mathematical circles for school students, served as an evaluation board member of school student mathematical competitions. Gave numerous talks on popular mathematics for various audiences, including lectures at training courses for teachers of mathematics; organised popular mathematics events. Published over 30 papers in major Ukrainian media on popular mathematics and science and education policies; gave numerous interviews for Ukrainian and international media, including major journals “Science” and “Nature”. A member of the Ukrainian initiative “UAScience.reload” facilitating assistance to Ukrainian researchers affected by the Russian aggression, and reconstruction of Ukrainian science potential.

**PUBLICATIONS**

1. **Yehorchenko**
**I.A., **Extension of Realisations for
Low-Dimensional Lie Algebras and Relative Differential Invariants,
arXiv:2212.05657

2.** Yehorchenko
I.A., **Eikonal
Equation 0.1, arXiv:2212.09914

3. ** Yehorchenko
I.A., **A.I.
Vorobyova, Conditional
and Hidden Infinite-Dimensional Symmetries of Wave Equations,
Ukrainian Mathematical Journal . Aug2022, Vol. 74 Issue 3, p.378-384.

4.** Yehorchenko
I.A., D**ifferential
invariants, hidden and conditional symmetry,
Ukr Math J 73, 1189–1199 (2022).

5. ** Yehorchenko
I.A., **Solutions
of the system of coupled eikonal equations, Collection of Papers of
the Institute of Mathematics of NAS of Ukraine, 2019, p.66-77.

6. **Yehorchenko
I.A., **Invariants
for sets of vectors and rank 2 tensors, and differential invariants
for vector functions, arXiv:1812.02918

7. **Yehorchenko
I.A., **General
Solution for a Coupled System of Eikonal Equations in Two Space
Variables,
arXiv:1712.01948

8. **Yehorchenko
I.A., **
Solutions
of the system of d'Alembert and eikonal equations, and classification
of reductions of PDEs, 2015 J. Phys.: Conf. Ser.
621 012018

9. **Yehorchenko
I.A., **
Ansatzes and exact solutions for nonlinear Schrodinger equations,
arXiv:1412.1889

10. **Yehorchenko**
**I.A.**,
Comment to" General Solution to
Unidimensional Hamilton-Jacobi Equation"[arXiv: 1302.0591 v1],
arXiv:1304.3515

11. **Yehorchenko**
**I.A. **Reduction of
Multidimensional Wave Equations to Two-Dimensional Equations:
Investigation of Possible Reduced Equations, Proceedings
of the 5th Workshop "Group Analysis of Differential Equations &
Integrable Systems", Protaras, Cyprus,
2011, p. 225-235, arXiv:1010.4977

12. **Yehorchenko**
**I.A. **Differential
Invariants and Hidden Symmetry,
arXiv:1010.5313

13. **Yehorchenko**
**I.A. **Conditional
Symmetry and Reductions for the Two-Dimensional Nonlinear Wave
Equation. I. General Case, arXiv:1010.4913

14. **Yehorchenko**
**I.A. **Reduction of
non-linear d'Alembert equations to two-dimensional equations,
Proceedings of the 4th Workshop "Group Analysis
of Differential Equations & Integrable Systems", Protaras,
Cyprus, 2009, p. 243-253,
arXiv:0910.2501

15. **Yehorchenko**
**I.A., **Vorobyova
A.I. Infinite-dimensional
symmetry for wave equation with additional condition,
arXiv:0910.2380

16. **Yehorchenko**
**I.A. **Differential
Invariants of Infinite-Dimensional Algebras That Are Equivalence
Algebras of Classes of PDE, Bulg. J. Phys.
vol.35 no.1 (2008), p. 481-488, arXiv:0910.2208

17. **Yehorchenko**
**I.A. **General Results
on Conditional Symmetry for the Two-Dimensional Nonlinear Wave
Equation, arXiv:0910.1946

18. **Yehorchenko**
**I.A. **Relative
invariants for Lie algebras: construction and applications, Symmetry
and Perturbation Theory, Proceedings of the International Conference
on SPT 2007. Otranto, Italy, 2 - 9 June 2007, G. Gaeta, R. Vitolo and
S. Walcher (Eds.), World Scientific (2007), p. 282-284

19. **Yehorchenko**
**I.A. **Reduction of
multidimensional non-linear d'Alembert equations to two-dimensional
equations: ansatzes, compatibility of reduction conditions,
Collection of Papers Dedicated to 70th Anniversary of
W.I. Fushchych, Kyiv, Institute of
Mathematics, 2006, p. 81-95, arXiv:math-ph/0611003

20. **Yehorchenko**
**I.A. **Differential
invariants for infinite-dimensional algebras, in *Proceedings*
*of the International Conference on SPT
2004*, Cala Gonone, Sardinia, Italy, May
30 – June 6, 2004; Editors G. Gaeta, B. Prinari, S.
Rauch-Wojciechowski and S. Terracini, World Scientific, 2005, p.
308-312 [pdf]
(see math-ph/0607002).

21. **Yehorchenko**
**I.A. **Group
classification with respect to hidden symmetry, in *Proceedings
of Fifth International Conference ``Symmetry in Nonlinear
Mathematical Physics''* (June 23-29,
2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A.
Yehorchenko, Kyiv, Institute of Mathematics, 2004, V.50, Part 1,
290-297 [pdf].

22. **Yehorchenko**
**I.A.**, Vorobyova
A.I. Sets of conditional symmetry operators and exact solutions for
wave and generalised heat equations., in *Proceedings
of Fifth International Conference ``Symmetry in Nonlinear
Mathematical Physics'' *(June 23-29,
2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A.
Yehorchenko, Kyiv, Institute of Mathematics, 2004, V.50, Part 1,
298-303 [pdf].

23. **Yehorchenko**
**I.A.** Differential
invariants and construction of conditionally invariant equations,
*Symmetry in nonlinear mathematical
physics, Part 1, Proceedings of Inst. Mathematics of National Acad.
Science of Ukraine (*Kyiv, 2001*)*,
2002, V. 43, 256-262 [pdf]
(see math-ph/0304029).

24. Popovych
R.O., **Yehorchenko**
**I.A.** Group
classification of generalized eikonal equations, *Ukrainian
Math. Journal*, 2001, V. 53, N 11,
1513-1520 (in Ukrainian); translation in Ukrainian Math. J., 2001, V.
53, N 11, 1841-1850 (see math-ph/0112055).

25. Vasilenko
O.F., **Yehorchenko**
**I.A.** Group
classification of multidimensional nonlinear wave equations, *Group
and analytic methods in mathematical physics, Proceedings of Inst.
Mathematics of National Acad. Science of Ukraine, *Kyiv,
2001, V. 36, 63-66 (in Ukrainian) [pdf].

26. **Yehorchenko**
**I.A.** On symmetry
of a class of first order PDEs, *Symmetry
in nonlinear mathematical physics, Part 1, 2, Proceedings of Inst.
Mathematics of National Acad. Science of Ukraine (*Kyiv,
1999*)*,
2000, V. 30, 245-248 [pdf].

27. **Yehorchenko**
**I.A.** Ansatzes and
exact solutions for nonlinear Schrödinger and wave equations,
*Symmetry and analytic methods in
mathematical physics (in Ukrainian), Inst. Mathematics of National
Acad. Science of Ukraine, *Kyiv, 1998,
V. 19, 80-87 [pdf].

28. **Yehorchenko**
**I.A.** Differential
invariants for a nonlinear representation of the Poincaré
algebra. Invariant equations, *Symmetry
in nonlinear mathematical physics, Vol. 1, 2, National Acad. Science
of Ukraine* *(Kyiv), *1997,
200-205 [pdf].

29. **Yehorchenko**
**I.A. **New nonlinear
Poincare-invariant equations, Proceedings
of the XXI Colloquim "Group Theory the Physics", Goslar,
Germany, 1996, World Scientific,
1997, p. 1022-1026

30. **Yehorchenko**
**I.A.** Second-order
differential invariants for some extensions of the Poincaré
group and invariant equations, *J.
Nonlin. Math. Phys.*, 1996, V. 3, no.
1-2, 186-195 [pdf].

31. Fushchych
W.I. and **Yehorchenko**
**I.A.** New
conditionally invariant solutions for non-linear d'Alembert equation,
Preprint LiTH–MAT–R–93–07,
Linköping University, Sweden, 1993, 9
p. [pdf].

32.
**Y****ehorchenko**
**I.A.** Second-order
differential invariants for the Poincaré, Galilei and
conformal algebras in many-dimensional spaces, *Classical
and quantum systems *(Goslar, 1991),
World Sci. Publishing, River Edge, NJ, 1993, 738-741.

33. **Yehorchenko**
**I.A.** Nonlinear
representation of the Poincaré algebra and invariant
equations, S*ymmetry analysis of
equations of mathematical physics, *Nat.
Acad. Sci. Ukraine, Inst. Math., Kyiv, 1992, 62-65.

34. Fushchych
W.I. and **Yehorchenko**
**I.A.**
Second-order differential invariants of the rotation group O(n) and
of its extensions: E(n); P(1,n); G(1,n), *Acta*
*Appl. Math.*,
1992, V. 28, N 1, 69-92 [pdf].

35.** ****Yehorchenko**
**I.A.**, Vorobyova
A.I. Conditional invariance and exact solutions of the
Klein-Gordon-Fock equation, *Reports of
Acad. Science of Ukraine*, 1992, N 1,
19-22, 176 (in Ukrainian).

36. **Yehorchenko**
**I.A.**, Vorobyova
A.I. Conditional invariance and exact solutions of a nonlinear heat
equation, *Reports of Acad. Science of
Ukraine*, 1992, N 3, 20-22, 160 (in
Ukrainian).

37. Fushchych
W.I. and **Yehorchenko**
**I.A.**
Non-Lie ansätze and conditional symmetry of the nonlinear
Schrödinger equation, *Ukrainian
Math. Journal*, 1991, V. 43, N 12,
1620-1628 (in Ukrainian); translation in Ukrainian Math. J., 1991, V.
43, N. 12, 1507-1515 [pdf].

38. Fushchych
W.I., Zhdanov R.Z. and
**Yehorchenko**
**I.A.** On
the reduction of the nonlinear multi-dimensional wave equations and
compatibility of the d'Alembert-Hamilton system, *J.
Math. Anal. Appl.*, 1991, V. 161, N 2,
352-360 [pdf].

39. Fushchych
W.I., **Yehorchenko**
**I.A.**
Reduction and solutions of a nonlinear equation for the vector
potential, *Reports of Acad. Science of
Ukr. SSR, Ser. A*, 1991, N 4, 23-25, 158
(in Ukrainian) [pdf].

40. **Yehorchenko**
**I.A.** Exact
solution of the non-linear d'Alembert equation. In the book:
Symmetries and Algebraic Structures in Physics,
Proceedings of the XVIII International Colloquium on Group
Theoretical Methods in Physics, Moscow, USSR, June 4-9, 1990, Vol. 2,
V.V. Dodonov. and V. Man'ko Eds, Nova Science, Singapore,
1991, p.55-58 (see on GoogleBooks)

41. Fushchych
V.I., **Yehorchenko**
**I.A.**
Reduction of a multidimensional nonlinear wave equation to
two-dimensional equations, *Reports of
Acad. Science of Ukr. SSR, Ser. A*,
1990, N 8, 32-34, 86 (in Ukrainian) [pdf]
(see math-ph/0610020).

42. **Yehorchenko**
**I.A.** Differential
invariants of Euclidean algebra, *Ukrainian
Math. Journal*, 1990, V. 42, N 6,
767-772 (in Ukrainian); translation in Ukrainian Math. J., 1990, V.
42, no. 6, 676-681.

43. **Yehorchenko**
**I.A.** Stationary
solutions of the nonlinear wave equation, *Algebra-theoretic
analysis of equations in mathematical physics, Acad. of Science of
Ukr. SSR, Institute* *of Mathematics,
Kyiv*, 1990, 26-30 (in Russian).

44. **Yehorchenko**
**I.A.** Exact
solutions of the nonlinear Schrödinger equation, *Symmetry
and solutions of equations of mathematical physics*,
Acad. of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1989, 17-20
(in Russian).

45. **Yehorchenko**
**I.A.** Symmetry
properties of nonlinear equations for a complex vector field, Acad.
Science of Ukr. SSR, Kyiv, Inst. Mat. Preprint N 89.48, 1989, 39 p.
(in Russian).

46. Fushchych
W.I. and **Yehorchenko**
**I.A.**
Differential invariants of the Poincaré algebra and of the
conformal algebra, *Reports of Acad.
Science of Ukr. SSR, Ser. A*, 1989, N 5,
21-22 (in Ukrainian) [pdf].

47. Fushchych
W.I. and **Yehorchenko**
**I.A.**
Differential invariants of the Galilei algebra, *Reports
of Acad. Science of Ukr. SSR, Ser. A*,
1989, N 4, 29-32, 86 (in Ukrainian) [pdf].

48. Fushchych
W.I. and **Yehorchenko**
**I.A.** The
symmetry and exact solutions of the nonlinear d'Alembert equation for
complex fields, *J. Phys. A*,
1989, V. 22, N 14, 2643-2652 [pdf].

49. **Yehorchenko**
**I.A.**, Vorobyova
A.I. Exact solutions of the wave equation with additional conditions,
*Symmetry and solutions of equations of
mathematical physics, *Acad. of Science
of Ukr. SSR, Inst. Mathematics, Kyiv, 1989, 21-25 (in Russian).

50. **Yehorchenko**
**I.A.** Complex
generalization of the Hamilton-Jacobi equation and its solutions,
*Symmetry analysis and solutions of
equations of mathematical physics, *Acad.
of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1988, 4-8 (in
Russian).

51. Fushchych
W.I., **Yehorchenko**
**I.A.**
Symmetric properties of complex-valued nonlinear wave equations,
*Reports of Acad. Science of USSR*,
1988, V. 298, N 2, 347-351 (in Russian) [pdf];
translation in Soviet Phys. Report, 33 (1988), N 1, 36-38.

52. **Yehorchenko**
**I.A.** Particular
solutions of two systems of nonlinear multidimensional wave
equations, *Symmetry and solutions of
nonlinear equations of mathematical physics, *Acad.
of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1987, 47-54 (in
Russian).

53. **Yehorchenko**
**I.A.** Poincaré-invariant
quasilinear wave equations for complex-valued functions, Acad.
Science of Ukr. SSR, Kyiv, Inst. Mat., Preprint N 87.3, 1987, 27 p.
(in Russian).

54. **Yehorchenko**
**I.A.** On the group
classification of equations for a complex vector potential,
*Group-theoretic investigations of the
equations of mathematical physics*,
Acad. of Science of Ukr. SSR, Inst. Mathematics,
Kyiv, 1985, 66-70 (in Russian).